Verify that a Hilbert space orthonormal basis in a finite dimensional Hilbert space is the same as an orthonormal basis in the sense of linear algebra.
Here is what I know. Hilbert space orthonormal basis is defined to be an orthonormal set such that the closure of its span is dense. But in finite dimensional case the span is closed already.
What exactly do I need to show now. This question seems quite straightforword but I do not know what to do next. Could anyone help me, please? Thank you!